Question

Find the rational roots of equation

i) x3-x2-9x+9=0 ii) 2x3-3x2-11x+6=0​

Answer 1

Answer:

$i) \: {x}^{3} - {x}^{2} - 9x + 9 = 0 \\ {x}^{2} (x - 1) - 9(x - 1) = 0 \\ ({x}^{2} - 9)(x - 1) = 0 \\\boxed{ x = ±3 \: , \: 1} \\ \boxed{x = 3 , \: - 3, \: 1 }\\ ii) \: 2 {x}^{3} - 3 {x}^{2} - 11x + 6 = 0 \\ x(2 {x}^{2} - 3x - 11)= - 6 \\or, \: \: \boxed{x = - 6} \\ or, \: \: 2 {x}^{2} - 3x - 11= - 6 \\ x(2x - 3) = 5 \\ or, \: \: \boxed{x = 5} \\ or, \: \: 2x - 3 = 5 \\ 2x = 8 \\ \boxed{x = 4} \\ \\ \red{\mathfrak{ \large{\underline{{Hope \: It \: Helps \: You}}}}} \\ \blue{\mathfrak{ \large{\underline{{Mark \: Me \: Brainliest}}}}}$